An attorney for Jesse Ventura asked a federal jury Tuesday to award the former Minnesota governor millions of dollars in damages for what he claimed is a lie in a memoir by the late military sniper Chris Kyle of Texas.

Ventura testified during the two-week trial that Kyle fabricated a passage in his 2012 bestseller American Sniper about punching Ventura in a California bar in 2006 after Ventura insulted Navy SEALs. But Kyle said in testimony videotaped before his death last year that his story was accurate.

Kyle of Midlothian and a friend were killed at a Glen Rose gun range last year. His widow, Taya Kyle, is executor of his estate with control over proceeds from book royalties and movie rights.

In his closing argument, Ventura attorney David Bradley Olson said he believes that Kyle’s estate has earned more than $6 million from the book, and suggested that $5 million to $15 million would be reasonable compensation for what he said was irreparable harm to Ventura’s reputation.

“The verdict will tell the world Chris Kyle’s story was a lie,” Olson said.

The jury deliberated for about 4 1/2 hours before stopping for the day and was to return today to continue.

Olson said Kyle’s claims that Ventura said he hated America, thought the U.S. military was killing innocent civilians in Iraq and that the SEALs “deserve to lose a few” had made him a pariah in the community that mattered most to him — the brotherhood of current and former SEALs.

“1.5 million people have bought the book,” he said. “Millions more heard Fox TV trash Jesse Ventura because of it. And the story went viral on the Internet and will be there forever.”

Ventura would never have said any of the remarks attributed to him because he remains proud of his and his parents’ military service, Olson said.

“The statement is completely out of character for Jesse Ventura,” he said.

But defense attorney John Borger told jurors in his own closing argument that Ventura failed to prove his claim that Kyle made up the story, and didn’t prove he suffered financially because of the book. He said the 11 witnesses presented by the defense “tell a compelling and consistent story” that backed Kyle’s version.

Legal experts have said Ventura has to clear a high legal bar to win, since as a public figure he must prove “actual malice.” According to the jury instructions, Ventura had to prove that Kyle either knew or believed what he wrote was untrue, or that he harbored such serious doubts that he acted with reckless disregard for the truth.